HWK 3-1.

E at A. (After you draw the frame of reference, and free body diagram for point A, determine that the direction of the electric field at A is toward the Cl ^- ion. It's magnitude is

E_A = k(3e)/(300 nm)² + k(e) / (100 nm)² = .192 x 10¹⁰ N/C

E at B. Since E is proportional to Q and inversely proportional to the square of distance, the electric field at B due to the Cl^- ion will be stronger than that due to the Fe ion, hence, the direction of the net electric field at B will again be toward the Cl^- ion, and it's magnitude will be

E_B = k(3e)/(500 nm)² + k(e)/(100 nm)² = .16 x 10¹⁰ N/C

HWK 3-2.

a)

E_He = E_p

k(2e)/(x_He)² = k(e)/(x_p)² implies that x_p = x_He / Ã2

b)

k(2e)/(x_He)² = k(e)/(x_e)² implies that x_e = x_He / Ã2

HWK 3-4.

a) Instructions for the crew member:

1. Release the charge to see which way it goes, but catch it before it gets away. Record this direction according to the fixed stars.

2. Place the meterstick in the direction the charge Q will travel.

3. Release the charge Q at one end of the meterstick and record the time it takes to reach the other end of the meterstick.

4. Return to the ship with the data.

b) The direction of the electric field is the direction noted by the crew member.

Assuming this electric field is constant in this region, then the acceleration due to this field will be too. So distance(D) travelled = .5 a (Dt)2, and from this a = 2D/(Dt)2, and D = 1 m in this case.

So, the magnitude of the electric field is E = F_E / Q = ma / Q = m 2(1m)/(Dt)²

HWK 3-5.